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The classification of non-singular actions, revisited

Published online by Cambridge University Press:  19 September 2008

Y. Katznelson  and
B. Weiss
Y. Katznelson
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA
B. Weiss
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel
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Abstract

A simpler treatment is given of the theorems of Dye and Krieger concerning the classification of non-singular ergodic transformations up to orbit equivalence.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 2 , June 1991 , pp. 333 - 348
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

[1]Dye, H.. On groups of measure preserving transformations, I; II. Amer. J. Math. 81 (1959), 119–159; 85 (1963), 551–576.Google Scholar
[2]Connes, A., Feldman, J. & Weiss, B.. An amenable equivalence relation is generated by a single transformation. Ergod. Th. & Dynam. Sys. 1 (1981), 431–450.CrossRefGoogle Scholar
[3]Hawkins, J.. Non-ITPFI diffeomorphisms. Israel J. Math. 42 (1982), 117–131.CrossRefGoogle Scholar
[4]Katznelson, Y.. Lectures on Orbit Equivalence. Mimeographed notes, Orsay (1980).Google Scholar
[5]Katznelson, Y. & Weiss, B.. Commuting measure preserving transformations. Israel J. Math. 12 (1972), 161–173.Google Scholar
[6]Krieger, W.. On non-singular transformations of a measure space, I; II. Z. Wahrsch, Th. 11 (1969), 83–97; 98–119.CrossRefGoogle Scholar
[7]Krieger, W.. On ergodic flows and isomorphism of factors. Math. Annalen 223 (1976), 19–70.CrossRefGoogle Scholar
[8]Maharam-Stone, D.. Incompressible transformations. Fund. Math. 56 (1964), 35–50.Google Scholar
[9]Weiss, B.. Orbit equivalence of non-singular actions. Théorie Ergodique, Monog. de l'Enseignement Math. 29 (1981), 77–107.Google Scholar